An Efficient Localized RBF-FD Method to Simulate the Heston–Hull–White PDE in Finance
Tao Liu,
Malik Zaka Ullah,
Stanford Shateyi,
Chao Liu,
Yanxiong Yang
Affiliations
Tao Liu
School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066000, China
Malik Zaka Ullah
Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Stanford Shateyi
Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South Africa
Chao Liu
School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066000, China
Yanxiong Yang
Eighth Geological Brigade of Hebei Bureau of Geology and Mineral Resources Exploration, Qinhuangdao 066000, China
The Heston–Hull–White three-dimensional time-dependent partial differential equation (PDE) is one of the important models in mathematical finance, at which not only the volatility is modeled based on a stochastic process but also the rate of interest is assumed to follow a stochastic dynamic. Hence, an efficient method is derived in this paper based on the methodology of the localized radial basis function generated finite difference (RBF-FD) scheme. The proposed solver uses the RBF-FD approximations on graded meshes along all three spatial variables and a high order time-stepping scheme. Stability is also studied in detail to show under what conditions the proposed method is stable. Computational simulations are given to support the theoretical discussions.
